Abhranti.ai
Explore
Start free

Tales by Dots and Lines: questions with answers

Class 8 Maths, Chapter 12 (NCERT). 15 questions by concept, 15 with pictures. Open “Show answer” for the answer and why.

How to teach this chapter · Common misconceptions & worked visual for this chapter

Combined changes and the mean

Question 1

Two new values shown are each 2 below the original mean, 9. What third value must be added to keep the mean unchanged?

Original17 values:2.5,5,6.5,7,7.5,four8s,9,10,10.5,11,two12s,13,15; original mean9. Two known new values are below9, by 2 and 2 respectively. The third new value is not plotted.Original collection: mean 923456789101112131415Known addition 12Known addition 22Third added value: ?
  1. (a)11
  2. (b)13
  3. (c)5
  4. (d)4
Show answer

(b) 13

The two known additions are 7 and 7. Three added values must sum to 27, so the third is 27 - 14 = 13.

Mean and median with frequencies

Question 2

What is the mean of the observations in this frequency dot plot?

Frequency dot plot. value0:frequency1, value1:frequency5, value2:frequency1, value3:frequency1, value4:frequency1, value5:frequency1Each dot is one observation012345678910
  1. (a)2.5
  2. (b)1.0
  3. (c)1.9
  4. (d)0.0
Show answer

(c) 1.9

The ten observations total 19, counting all five dots at 1. Their mean is 19 divided by 10, or 1.9.

Mean as the unique balance point

Question 3

The marked centre balances the distances. What is the sum of the distances from the dots to its left?

Dots at 2, 4, 9. Centre 5. Separate arrows show distances; repeated dots are separate observations.234567891011121314151617Centre = 5
  1. (a)3
  2. (b)5
  3. (c)4
  4. (d)8
Show answer

(c) 4

The distances to 2 and 4 are 3 and 1. Their sum is 4, equal to the distance from 5 to 9.

Mean grids

Question 4

Each row and column has mean 10. Which lines fail to have mean 10?

Mean grid. rows 6, 13, 11; 10, 8, 12; 14, 9, 761311108121497
  1. (a)no lines
  2. (b)only the middle column
  3. (c)only the middle row
  4. (d)both diagonals
Show answer

(d) both diagonals

The diagonals total 21 and 33, giving means 7 and 11. Each row and column totals 30.

Uniform scaling of the mean

Question 5

Every original value is multiplied by 2. What is the new mean, rounded to the nearest hundredth?

Original values3,4,5,6,7,7,8,8,8,10,13 and their scaled values on equal0 to65 axes. Every original observation remains represented.05101520253035404550556065Original values05101520253035404550556065Every value multiplied by 23, 4, 5, 6, 7, 7, 8, 8, 8, 10, 13Both axes use the same scale
  1. (a)3.59
  2. (b)14.36
  3. (c)9.18
  4. (d)7.18
Show answer

(b) 14.36

Doubling every value doubles the total from 79 to 158. The count stays eleven, so the new mean is 158/11158/11, approximately 14.36.

Means on dot plots

Question 6

What is the mean of the four plotted values?

Dots at 10, 10, 11, 17. Each stacked dot is counted separately.02468101214161819Each dot is one value
  1. (a)13.5
  2. (b)10.0
  3. (c)17.0
  4. (d)12.0
Show answer

(d) 12.0

The four values sum to 48, including both dots at 10. Dividing by 4 gives 12.

Verify and complete a dot plot

Question 7

One dot is missing from the plot. The completed collection has mean 9. What is the missing value?

Ten shown values: 4,7,8,8,9,9,9,9,9,11. The missing dot is not drawn.Ten shown values; one dot is missing0246810121416
  1. (a)16
  2. (b)9
  3. (c)7
  4. (d)4
Show answer

(a) 16

The ten shown values total 83. Eleven values with mean 9 must total 99, so the missing value is 16.

Adding or subtracting the same amount

Question 8

Each of the eleven values increases by 3. What is the new mean, rounded to the nearest hundredth?

Top values: 3,4,5,6,7,7,8,8,8,10,13. Bottom adds 3 to each top value. Repeated dots are stacked.Each dot is one valueBefore024681012141618202224Every value +3024681012141618202224
  1. (a)7.18
  2. (b)10.18
  3. (c)6.91
  4. (d)7.45
Show answer

(b) 10.18

The original sum is 79. Adding 3 to each of eleven values gives total 112, so the new mean is 112/11112/11, approximately 10.18.

Mean after including or removing one value

Question 9

One value, 6, is included in the four-value collection. What is the new mean?

Before: 5, 5, 10, 24. Each stacked dot is counted separately. After include: 5, 5, 10, 24, 6.Each dot is one valueBefore4681012141618202224After including 64681012141618202224
  1. (a)11.0
  2. (b)12.0
  3. (c)6.0
  4. (d)10.0
Show answer

(d) 10.0

The original sum is 44. Including 6 gives a sum of 50 across five values, so the mean is 10.

Choosing a graph representation

Question 10

How does the information in the column graph compare with the information in the line graph?

Aligned columns above, lines below; Jan-Dec, Celsius0-40. Approximate Kerala hollow bars/circles: 30.5,31.5,32.5,33,32,30.5,28.8,29.1,29.5,30,31,31. Punjab centre-marked bars/squares: 19,26,29,34,37,38,34.5,35,35.5,33,28,23.Monthly maximum temperature (approximate)Kerala: hollow bars / circlesPunjab: centre-marked bars / squaresColumns — temperature in Celsius02040Lines — temperature in Celsius02040JanFebMarAprMayJunJulAugSepOctNovDec
  1. (a)monthly observations in columns but yearly observations in lines
  2. (b)temperatures in columns but student counts in lines
  3. (c)different temperature observations created by joining points
  4. (d)the same monthly observations in different forms
Show answer

(d) the same monthly observations in different forms

Each month has one value for Kerala and one for Punjab in both graphs. Changing the drawing does not change those observations.

Interpreting published graphs

Question 11

Which interval shows the larger increase in the USA count of objects launched?

Approximate annual objects launched,2012–2024. Series labelled directly. World and China solid; USA and Russia dashed.Objects launched into space01000200030002012201420162018202020222024WorldUSAChinaRussiaApproximate source readings; solid / dashed series
  1. (a)2023 to 2024
  2. (b)A decrease in both intervals
  3. (c)2022 to 2023
  4. (d)Equal increases
Show answer

(c) 2022 to 2023

The USA segment from 2022 to 2023 is much steeper. The higher final point in 2024 does not mean that its preceding increase was larger.

Median positions and changes

Question 12

Include 11 in the collection 4, 7, 8, 12, 14. What is the median of the six values?

Dots at 4, 7, 8, 11, 12, 14. Every repeated dot counts separately; no median marker is shown.Each dot is one value0246810121416
  1. (a)8
  2. (b)11
  3. (c)14
  4. (d)9.5
Show answer

(d) 9.5

The ordered values are 4, 7, 8, 11, 12, 14. The third and fourth values are 8 and 11, whose average is 9.5.

Read line series and changes

Question 13

The graph shows sample temperatures for practice. What is the June temperature of the square series?

Practice monthly maximum temperatures. Jan through Dec. Circle series: 30,31,32,33,32,30,29,30,30,31,31,31. Square series: 18,22,26,30,34,36,32,33,34,30,25,21. Circle and square markers distinguish the series.Practice monthly maximum temperaturesCircle seriesSquare series°C0510152025303540JanFebMarAprMayJunJulAugSepOctNovDec
  1. (a)36
  2. (b)32
  3. (c)30
  4. (d)34
Show answer

(a) 36

Follow June to the square marker, then read its height: 36°C. The circle marker at June shows 30°C and belongs to the other series.

Reading sun and moon clock graphs

Question 14

In this sample, the middle sunset is three five-minute intervals after 18:00. Sunrise is 06:00. What is the middle day’s length in minutes?

Sample adjacent daysA,B,C. Sunrise06:05,06:00,05:55. Sunset17:55,18:00,18:05 plus 3 five-minute steps. Separate morning/evening panels.Sample clock times: three adjacent daysSunrise panel05:5005:5506:0006:0506:10AB (middle)CSunset panel17:5017:5518:0018:0518:1018:1518:2018:2518:3018:3518:40AB (middle)CSmall grid intervals are five minutesSample times, not a recorded location
  1. (a)723 minutes
  2. (b)705 minutes
  3. (c)735 minutes
  4. (d)750 minutes
Show answer

(c) 735 minutes

From 06:00 to 18:00 is 720 minutes. Three five-minute intervals add 15 minutes, giving 735 minutes of daylight.

Tables and line-graph values

Question 15

Using the exact table entries, what is Mangaluru’s total average number of rainfall days over the twelve months?

Exact monthly rainfall-day table for Mangaluru, Port Blair and Rameswaram.Exact table values: average rainfall daysMonthMangaluruPort BlairRameswaramJan0.12.42.6Feb01.31.3Mar0.10.91.9Apr1.83.33.4May6.215.52.5Jun24.118.70.4Jul27.717.31Aug24.518.81Sep1416.81.9Oct8.814.18.1Nov3.911.310.4Dec0.95.47.8
  1. (a)112.1
  2. (b)112
  3. (c)42.3
  4. (d)125.8
Show answer

(a) 112.1

Adding Mangaluru’s twelve exact entries gives 112.1 days. Do not replace them with rounded plotting values when an exact-table total is requested.

Common misconception in Tales by Dots and Lines

Open full misconception guide →

Can the average come from just the smallest and largest values?

Wrong

The mean of 2, 2, 2 and 10 is 6.

Why it feels right. I averaged the two endpoints on the plot.

Right

Every observation contributes to the mean.

Worked example

Three observations sit at 2 and only one sits at 10. The mean is 4, closer to the cluster.
  1. Place three dots at 2 and one at 10.
  2. The mean is (2 + 2 + 2 + 10) ÷ 4 = 4.